Magnetic chitosan/Cu–Mg–Al layered double hydroxide (mCSLDH) nanocomposite was prepared and copper(II) ions were immobilized in the prepared composite. The nanocomposite [(Cu-mCSLDH)] was characterized by FT-IR, XRD, VSM, AAS, EDX, SEM and TEM. The utility of nanocomposite was investigated in the one-pot three-component (A3) coupling of aldehydes, amines and alkynes to produce propargylamines. The Cu-mCSLDH nanocomposite is found to be highly efficient and recyclable heterogeneous catalyst.